6 papers
Non-kinetic homotopy coherent actions on four-manifolds
Sungkyung Kang, JungHwan Park, Masaki Taniguchi
We give the first example of a non-kinetic smooth homotopy coherent action of order two on a closed simply connected smooth four-manifold. This action is obtained by restricting a…
Exotic diffeomorphisms on a contractible 4-manifold surviving two stabilizations
Sungkyung Kang, JungHwan Park, Masaki Taniguchi
We develop a -equivariant refinement of the lattice homotopy type for computing equivariant Seiberg--Witten Floer homotopy types. As an applica…
Smooth concordance of cables of the figure-eight knot
Sungkyung Kang, JungHwan Park, Masaki Taniguchi
We prove that every nontrivial cable of the figure-eight knot has infinite order in the smooth knot concordance group. Our main contribution is a uniform proof that applies to all…
Cables of the figure-eight knot via real Frøyshov invariants
Sungkyung Kang, JungHwan Park, Masaki Taniguchi
We prove that the -cable of the figure-eight knot is not smoothly slice when is odd, by using the real Seiberg-Witten Frøyshov invariant of Konno-Miyazawa-Taniguchi. F…
A satellite formula for real Seiberg-Witten Floer homotopy types
Jin Miyazawa, JungHwan Park, Masaki Taniguchi
We establish a satellite formula for the real Seiberg-Witten Floer homotopy types of knots with odd patterns. Using this, we derive several applications to knot concordance theory.…
On the connected sums of the -cable of the figure eight knot
Yoshihiro Fukumoto, Masaki Taniguchi
We show that the 3-fold (resp. 6-fold) connected sum of the -cable of the figure-eight knot cannot bound a smooth null-homologous disk in a punctured (resp.…